Nonparametric tests of structure for high angular resolution diffusion imaging in Q-space

High angular resolution diffusion imaging data is the observed characteristic function for the local diffusion of water molecules in tissue. This data is used to infer structural information in brain imaging. Nonparametric scalar measures are proposed to summarize such data, and to locally characterize spatial features of the diffusion probability density function (PDF), relying on the geometry of the characteristic function. Summary statistics are defined so that their distributions are, to first-order, both independent of nuisance parameters and also analytically tractable. The dominant direction of the diffusion at a spatial location (voxel) is determined, and a new set of axes are introduced in Fourier space. Variation quantified in these axes determines the local spatial properties of the diffusion density. Nonparametric hypothesis tests for determining whether the diffusion is unimodal, isotropic or multi-modal are proposed. More subtle characteristics of white-matter microstructure, such as the degree of anisotropy of the PDF and symmetry compared with a variety of asymmetric PDF alternatives, may be ascertained directly in the Fourier domain without parametric assumptions on the form of the diffusion PDF. We simulate a set of diffusion processes and characterize their local properties using the newly introduced summaries. We show how complex white-matter structures across multiple voxels exhibit clear ellipsoidal and asymmetric structure in simulation, and assess the performance of the statistics in clinically-acquired magnetic resonance imaging data.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS441 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Mass Functions of Supermassive Black Holes Across Cosmic Time

The black hole mass function of supermassive black holes describes the evolution of the distribution of black hole mass. It is one of the primary empirical tools available for mapping the growth of supermassive black holes and for constraining theoretical models of their evolution. In this review we discuss methods for estimating the black hole mass function, including their advantages and disadvantages. We also review the results of using these methods for estimating the mass function of both active and inactive black holes. In addition, we review current theoretical models for the growth of supermassive black holes that predict the black hole mass function. We conclude with a discussion of directions for future research which will lead to improvement in both empirical and theoretical determinations of the mass function of supermassive black holes.Comment: 40 pages, 7 figures, review paper accepted for the Advances in Astronomy Special Issue "Seeking for the Leading Actor on the Cosmic Stage: Galaxies versus Supermassive Black Holes

Functionally referential signals: a promising paradigm whose time has passed

Finding the evolutionary origins of human language in the communication systems of our closest living relatives has, for the last several decades, been a major goal of many in the field of animal communication generally and primate communication specifically.1–4 The so-called “functionally referential” signals have long been considered promising in this regard, with apparent parallels with the semantic communication that characterizes language. The once-prominent idea that functionally referential signals are word-like, in that they are arbitrary sounds that refer to phenomena external to the caller, has largely been abandoned.5 However, the idea that these signals may offer the strongest link between primate communication and human language remains widespread, primarily due to the fact the behavior of receivers indicates that such signals enable them to make very specific inferences about their physical or social environment. Here we review the concept of functional reference and discuss modern perspectives that indicate that, although the sophistication of receivers provides some continuity between nonhuman primate and human cognition, this continuity is not unique to functionally referential signals. In fact, because functionally referential signals are, by definition, produced only in specific contexts, receivers are less dependent on the integration of contextual cues with signal features to determine an appropriate response. The processing of functionally referential signals is therefore likely to entail simpler cognitive operations than does that of less context-specific signals. While studies of functional reference have been important in highlighting the relatively sophisticated processes that underlie receiver behavior, we believe that the continued focus on context-specific calls detracts from the potentially more complex processes underlying responses to more unspecific calls. In this sense, we argue that the concept of functional reference, while historically important for the field, has outlived its usefulness and become a red herring in the pursuit of the links between primate communication and human language

Dynamics and Thermodynamics of a Novel Phase of NaAlH4

We characterize a novel orthorhombic phase (gamma) of NaAlH4, discovered using first-principles molecular dynamics, and discuss its relevance to the dehydrogenation mechanism. This phase is close in energy to the known low-temperature structure and becomes the stabler phase above 320 K, thanks to a larger vibrational entropy associated with AlH4 rotational modes. The structural similarity of gamma-NaAlH4 to alpha-Na3AlH6 suggests it acts as a key intermediate during hydrogen release. Findings are consistent with recent experiments recording an unknown phase during dehydrogenation.Comment: 10 pages, 4 figures, 1 table + supplementary info; In press (Physical Review Letters

Neuroscience, Spiritual Formation, and Bodily Souls: A Critique of Christian Physicalism

The link between human nature and human flourishing is undeniable. "A healthy tree cannot bear bad fruit, nor can a diseased tree bear good fruit" (Matt. 7:18). The ontology of the human person will, therefore, ground the nature of human flourishing and thereby sanctification. Spiritual formation is the area of Christian theology that studies sanctification, the Spirit-guided process whereby disciples of Jesus are formed into the image of Jesus (Rom. 8:28-29; 2 Cor. 3:18; 2 Peter 3:18). Until the nineteenth century, there was an overwhelming consensus among Christian thinkers that some form of mind-body (or soul-body) dualism is true of human beings. Recently, that consensus has eroded, and with it the availability of a shared body of knowledge about spiritual formation. Some Christian physicalists argue that dualism is incompatible with central elements of spiritual formation. Neuroscientist Warren Brown and psychologist Brad Strawn offer the only substantive account of spiritual formation from the view of Christian physicalism and its accompanying objections to dualism. It is on their arguments that this chapter focuses. We argue that Brown and Strawn fail to support their incompatibility thesis. Additionally, we argue that Christian physicalism stands in tension with important philosophical and theological foundations of Christian spiritual formation. In doing so we offer a specific form of dualism, the bodily soul view, and explain how this view illuminates the importance of embodiment, our neurological and social development, and hence the important physical aspects of Christian spiritual formation